Forcing the user to use their device in a certain way, based on your subjective opinion of what is best, is a rude design. Any usability gain that comes from landscape mode will be more than offset by the bad will generated by taking control away from the user. Philosophically, this is just a bad idea, apart from any concrete consequences.
And there will also be many consequences.
Usability consequences.
- People using mobile devices are often on the go, carrying things, etc. A minor inconvenience of changing one's phone orientation might be a real pain, depending on the circumstances.
- It interrupts people's work flow. Suppose they want to switch back and forth between your site and other sites or apps. Now they have to use other apps in what may not be their preferred orientation, or keep switching back and forth.
- In some cases, switching orientation may not be easy, or may not even be possible:
- The device may be in a dock or stand.
- Some users disable automatic screen rotation, because they find it annoying. These users would have to go into their settings and make a change to use your site (then go back into their settings later to change it back).
- Disabled users may have the device mounted on something and not be physically able to change it.
Technical consequences:
- Surely this goes against design guidelines on all platforms.
- How do you implement it?
- Do you just display the site in landscape regardless? This is confusing and may even be perceived as an error. It will also conflict with the web browser's navigation.
- Display a message asking the user to rotate their device? This adds an annoying extra step (and what do you do if they rotate their device back later? Go back to this message repeatedly?)
- Since this is only needed for one part of your site, which may not be used, you are faced with the unappealing choice of forcing this on the entire site for no apparent reason, or breaking the flow of your own website to enforce it.
- It doesn't appear to even give you much benefit, since the user may have to scroll to see the whole thing even in landscape mode.
In conclusion: absolutely, do not do this. Seat selection may not be the easiest to navigate in portrait mode, but users realize that they can change the device orientation if they want to see more on the screen. Let them make that decision.